Finite Group Databasebeta

← #20244163

Subgroups — #20244163

Order 6016.

200 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 97 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13093959C212yesmaximal
2#15689147C211yesmaximal, characteristic
3C2×C4⋊(C47⋊C8)C211yesmaximal, characteristic
4#15688887C212yesmaximal
5C4×M16×C47C211yesmaximal, characteristic
6C2×#10625329C2212yes—
7C22×C47⋊C8C2212yes—
8#13093959—24no—
9C4⋊(C47⋊C8)—21no—
10C4⋊(C47⋊C8)—21no—
11C4⋊(C47⋊C8)C412yes—
12C4⋊(C47⋊C8)C412yes—
13C2×M16×C47C2211yescharacteristic
14C2×M16×C47C2211yescharacteristic
15C2×C42×C47C2211yescharacteristic
16#97×C47—21no—
17C4×C8×C47—21no—
18C22×C4×C47Q811yescharacteristic
19C22×C4×C47Q811yescharacteristic
20C22×C4×C47C2311yescharacteristic
21M16×C47—21no—
22M16×C47—21no—
23M16×C47D412yes—
24M16×C47Q812yes—
25C2×C8×C47—21no—
26C2×C8×C47—21no—
27C42×C47C2×C411yescharacteristic
28C42×C47C2×C411yescharacteristic
29C42×C47D411yescharacteristic
30C42×C47D411yescharacteristic
31#10625329—22no—
32#10625329—22no—
33C2×C47⋊C8—22no—
34C2×C47⋊C8—22no—
35C2×C47⋊C8—22no—
36C2×C47⋊C8C2×C414yes—
37C23×C47C2×Q811yescharacteristic
38C2×C4×C47—22no—
39C2×C4×C47—41no—
40C2×C4×C47C4⋊C411yescharacteristic
41C2×C4×C47C4⋊C411yescharacteristic
42C2×C4×C47C4⋊C411yescharacteristic
43C2×C4×C47C4⋊C411yescharacteristic
44C2×C4×C47C22×C411yescharacteristic
45C2×C4×C47C2×D411yescharacteristic
46C2×C4×C47C2×D411yescharacteristic
47C2×C4×C47C2×Q811yescharacteristic
48C2×C4×C47#4111yescharacteristic
49C2×C4×C47#4111yescharacteristic
50C8×C47—22no—
51C8×C47—22no—
52C47⋊C8—24no—
53C47⋊C8—42no—
54C22×C47—21no—
55C22×C47—21no—
56C22×C47C2×C4⋊C411yescharacteristic
57C22×C47#12511yescharacteristic
58C22×C47C4⋊Q811yescharacteristic
59C4×C47—21no—
60C4×C47—21no—
61C4×C47—21no—
62C4×C47#10812yescomplemented
63C4×C47C4×D411yescharacteristic
64C4×C47C4×Q811yescharacteristic
65C4×C47#12111yescharacteristic
66C4×C47C22⋊Q811yescharacteristic
67#1950—471nomaximal, Sylow
68C2×C47—21no—
69C2×C47—21no—
70C2×C47#38911yescharacteristic
71C2×C47C2×#10811yescharacteristic
72C2×C47#43011yescharacteristic
73C2×#108—472no—
74#423—471no—
75C2×C4⋊C8—471no—
76C4×M16D4711yescharacteristic
77#341—472no—
78C47#195011yescharacteristic, complemented, Sylow
79C2×M16—472no—
80C2×M16C2×D4711yescharacteristic
81C2×M16C2×D4711yescharacteristic
82C22×C8—472no—
83C2×C42C2×D4711yescharacteristic
84#108—944no—
85C4⋊C8—472no—
86C4⋊C8—472no—
87C4⋊C8—941no—
88C4⋊C8—941no—
89#97—21no—
90C4×C8—21no—
91C22×C4Dic9411yescharacteristic
92C22×C4Dic9411yescharacteristic
93C22×C4C22×D4711yescharacteristic
94M16—21no—
95M16—21no—
96M16—942no—
97M16—942no—
98M16Dic9412yes—
99M16D18812yes—
100C2×C8—21no—
101C2×C8—21no—
102C2×C8—474no—
103C2×C8—942no—
104C2×C8—942no—
105C2×C8—942no—
106C42C4×D4711yescharacteristic
107C42C4×D4711yescharacteristic
108C42C22⋊D4711yescharacteristic
109C42C22⋊D4711yescharacteristic
110C23C2×Dic9411yescharacteristic
111C2×C4—22no—
112C2×C4—41no—
113C2×C4Dic47⋊C411yescharacteristic
114C2×C4Dic47⋊C411yescharacteristic
115C2×C4Dic47⋊C411yescharacteristic
116C2×C4Dic47⋊C411yescharacteristic
117C2×C4C2×Dic9411yescharacteristic
118C2×C4C2×C4×D4711yescharacteristic
119C2×C4C2×D18811yescharacteristic
120C2×C4#1062535011yescharacteristic
121C2×C4#1062535011yescharacteristic
122C2×C4C2×C22⋊D4711yescharacteristic
123C8—22no—
124C8—22no—
125C8—944no—
126C8—1882no—
127C22—21no—
128C22—21no—
129C22C2×Dic47⋊C411yescharacteristic
130C22#1309401611yescharacteristic
131C22#1309402411yescharacteristic
132C4—21no—
133C4—21no—
134C4—21no—
135C4#1309395912yescomplemented
136C4C4×D18811yescharacteristic
137C4C4×Dic9411yescharacteristic
138C4#1309399811yescharacteristic
139C4#1309400311yescharacteristic
140C2—21no—
141C2—21no—
142C2#1568902111yescharacteristic
143C2C2×#1309395911yescharacteristic
144C2#1568917111yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊D47
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC4×M16×C47C2
socleC22×C47C2×C4⋊C4
hypercenterC4×M16D47
hypocenterC47#1950
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×M16

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
62. C4×C47#108semidirect
78. C47#1950semidirect
135. C4#13093959semidirect